Your soultion is a bunch of newly drafted marksdwarves with cheap wooden crossbows, and a ton of also cheap wooden or bone bolts.
=> free target practice, free kea meat, excessive fun for your denizens.
Keas only provide a skull when butchered, according to wiki *shrug*
In any case, they are lovely birds for giving a low-level multi-faceted challenge, and behave a lot like their larger cousins of giant keas, undead keas, giant undead keas, rocs and undead rocs.
Albeit their stealing can be highly annoying - especially if they steal your only anvil - and they can cause deaths when your fortress design gives them tactical advantage (trees, dodge-deaths) - or your chained up war dog has become depressed or sucks at war and fails to fight back - their main danger to fortresses is vengeful spirals, where every dwarf gets stress buildup from wanting revenge on them.
Overall, the simplest quick solution to keas involves 2 logs and 1 tanned hide done into wood bolts, wood crossbow and quiver:
0. See if you have any dwarf with "Hunt!" job or Hunter job title. There's your pre-trained marksdwarf (disable hunting labour first.) with crossbow, quiver and bolts already obtained.
1. Go to (m)ilitary menu and (c)reate squad (if you already have one, you need to appoint a new milita commander from (n)obles).
2. Pick "No uniform" and stick 1 dwarf you want to be alert for keas in it.
3. Go to equip screen and give them a crossbow from (W)eapons.
4. Go to (f)ammunition and allocate them 25 or 50 bolts. Note that if you have less bolts than is allocated for hunters(default 100, and pretty likely situation if you don't have any hunters), they will never pick up the bolts you currently have.*
5. Go to supplies menu and disable them from carrying food or drink so they will respond promptly.
6. Actual response, finally: escape all the way back to default screen, go into (s)quad menu and order your newly-created squad(press the letter before their name) to station at where keas approach your fortress.
*It can be better to hunt with with military on patrol rather than actual hunters on account of being able to give military armor, shields, specific patrol, not sleeping in dirt, not retreating for bolts, not ignoring every animal but the one they're hunting....In which case you want to disable hunting labor on anyone who you find hunting and set hunters ammunition to 0. Note that if you do this, dwarves need to have (o)rder to gather corpses from outside, or you'll not get the meat from this hunting (though hunters don't bring back more than 1 animal too, even if they kill several at once).
There are more complex⁑ solutions, of course.
If you have single entrance into a corridor, setting up a weapon trap into a diagonal spot (wooden trap components can work) with cage trap (perhaps few tiles) afterwards to capture any who were lucky or fast enough to fly over the trap can help you hunt keas to extinction (check with dfhack's region-pop list KEA).
Alternatively, building 20z+ tall tower of stairs and putting something worth stealing (masterwork bucket is fine) before such a trap on top might work (untested) to kill keas without dwarves ever seeing them.
On hostile tree attacks, using 10x10 farm plots/paved roads over your fort roof would give you nice quick checks with instant highlighting of holes.
For some entrances, walling up your main entrance and then having item to be stockpiled outside can also let you check if there is alternate "normal path".
Finally, pay in mind that flyers can path diagonally up or down and between missing floors - what is watertight is not keatight.
⁑ For dwarves. A player would likely find making 2 mechanisms, 1 wooden cage and few wooden trap components, then ordering them to be built simpler.